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        <a href=".." >DE-9IM模型</a>
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						<h1 id="&#x7A7A;&#x95F4;&#x5173;&#x7CFB;&#x3001;de-9im&#x548C;&#x8C13;&#x8BCD;">&#x7A7A;&#x95F4;&#x5173;&#x7CFB;&#x3001;DE-9IM&#x548C;&#x8C13;&#x8BCD;</h1>
<p><a href="https://docs.geotools.org/latest/userguide/library/jts/dim9.html" target="_blank">&#x5B98;&#x7F51;&#x6587;&#x6863;&#x5730;&#x5740;</a></p>
<p>&#x8981;&#x5224;&#x65AD;&#x4E24;&#x4E2A;&#x591A;&#x8FB9;&#x5F62;&#x7684;&#x5173;&#x7CFB;&#xFF0C;&#x5B9E;&#x9645;&#x4E0A;&#x5C5E;&#x4E8E;&#x51E0;&#x4F55;&#x56FE;&#x5F62;&#x7A7A;&#x95F4;&#x5173;&#x7CFB;&#x5224;&#x65AD;&#x3002;&#x51E0;&#x4F55;&#x56FE;&#x5F62;&#x5E76;&#x4E0D;&#x53EA;&#x6709;&#x591A;&#x8FB9;&#x5F62;&#x4E00;&#x79CD;&#xFF0C;&#x5B83;&#x5305;&#x62EC;&#x70B9;&#x3001;&#x7EBF;&#x3001;&#x9762;&#x6784;&#x6210;&#x7684;&#x4EFB;&#x4F55;&#x56FE;&#x5F62;&#xFF0C;&#x4E24;&#x4E24;&#x4E4B;&#x95F4;&#x76F8;&#x4E92;&#x5173;&#x7CFB;&#x4E5F;&#x6709;&#x5F88;&#x591A;&#x79CD;&#xFF0C;&#x56E0;&#x6B64;&#x7A7A;&#x95F4;&#x5173;&#x7CFB;&#x975E;&#x5E38;&#x590D;&#x6742;&#x3002;&#x6839;&#x636E;&#x524D;&#x4EBA;&#x7684;&#x7814;&#x7A76;&#xFF0C;&#x603B;&#x7ED3;&#x51FA;&#x4E86;DE-9IM&#x6A21;&#x578B;&#xFF0C;&#x4F5C;&#x4E3A;&#x4E00;&#x79CD;&#x7A7A;&#x95F4;&#x5173;&#x7CFB;&#x5224;&#x65AD;&#x7684;&#x6807;&#x51C6;&#x3002;</p>
<p>DE-9IM&#xFF0C;&#x5168;&#x79F0;&#x662F;<strong>Dimensionally Extended nine-Intersection Model (DE-9IM)</strong>&#xFF0C;&#x662F;&#x4E00;&#x79CD;&#x62D3;&#x6251;&#x6A21;&#x578B;&#xFF0C;&#x7528;&#x4E8E;&#x63CF;&#x8FF0;&#x4E24;&#x4E2A;&#x51E0;&#x4F55;&#x56FE;&#x5F62;&#x7A7A;&#x95F4;&#x5173;&#x7CFB;&#x7684;&#x4E00;&#x79CD;&#x6807;&#x51C6;&#x3002;&#x5728;&#x4E13;&#x4E1A;&#x9886;&#x57DF;&#xFF0C;&#x901A;&#x5E38;&#x5C06;&#x6BCF;&#x4E2A;&#x51E0;&#x4F55;&#x56FE;&#x5F62;&#x5206;&#x4E3A;&#x4E09;&#x90E8;&#x5206;&#xFF1A;&#x5916;&#x90E8;&#xFF08;exterior),&#x8FB9;&#x754C;&#xFF08;boundary)&#x548C;&#x5185;&#x90E8;(interior)&#x3002;&#x76F8;&#x50CF;&#x4E00;&#x4E0B;&#xFF0C;&#x4E00;&#x4E2A;&#x77E9;&#x5F62;&#x7684;&#x4E09;&#x4E2A;&#x90E8;&#x5206;&#x5206;&#x522B;&#x662F;&#x6307;&#x54EA;&#x4E9B;&#x5730;&#x65B9;&#xFF1F;&#x4E24;&#x4E2A;&#x56FE;&#x5F62;&#x7684;&#x5173;&#x7CFB;&#x5224;&#x65AD;&#xFF0C;&#x5B9E;&#x9645;&#x4E0A;&#x5C31;&#x662F;&#x4E09;&#x4E2A;&#x90E8;&#x5206;&#x7684;&#x5206;&#x522B;&#x5224;&#x65AD;&#xFF0C;&#x56E0;&#x6B64;&#x5C31;&#x4F1A;&#x6709;&#x4E00;&#x4E2A;3*3&#x4EA4;&#x53C9;&#x77E9;&#x9635;&#xFF0C;&#x8FD9;&#x4E2A;&#x77E9;&#x9635;&#x5C31;&#x662F;DE-9IM&#x6A21;&#x578B;&#xFF0C;&#x5982;&#x4E0B;&#x56FE;&#xFF1A;</p>
<p><strong>x</strong> INTERSECTION <strong>y</strong> =</p>
<table>
<thead>
<tr>
<th>9IM</th>
<th>Interior</th>
<th>Boundary</th>
<th>Exterior</th>
</tr>
</thead>
<tbody>
<tr>
<td>Interior</td>
<td>x0 INTERSECTION y0</td>
<td>x0 INTERSECTION dy</td>
<td>x0 INTERSECTION -y</td>
</tr>
<tr>
<td>Boundary</td>
<td>dx INTERSECTION y0</td>
<td>dx INTERSECTION dy</td>
<td>dx INTERSECTION -y</td>
</tr>
<tr>
<td>Exterior</td>
<td>-x INTERSECTION y0</td>
<td>-x INTERSECTION dy</td>
<td>-x INTERSECTION -y</td>
</tr>
</tbody>
</table>
<p><img src="../assets/de-9im.png" alt=""></p>
<p>&#x7F51;&#x53CB;&#x5206;&#x89E3;&#x56FE;</p>
<p><img src="../assets/de-9im2.jpg" alt=""></p>
<p>&#x5176;&#x4E2D;&#xFF0C;a,b&#x5206;&#x522B;&#x4EE3;&#x8868;&#x4E24;&#x4E2A;&#x9762;&#xFF0C;I,B,E&#x5206;&#x522B;&#x8868;&#x793A;&#x5B83;&#x7684;&#x4E09;&#x4E2A;&#x90E8;&#x5206;&#x3002;Dim()&#x51FD;&#x6570;&#x8868;&#x793A;&#x76F8;&#x4EA4;&#x90E8;&#x5206;&#x7684;&#x7EF4;&#x5EA6;&#x3002;&#x5982;&#x679C;&#x76F8;&#x4EA4;&#x90E8;&#x5206;&#x662F;&#x4E00;&#x4E2A;&#x9762;&#xFF0C;&#x5219;&#x662F;&#x4E8C;&#x7EF4;&#xFF0C;&#x5373;dim()=2&#xFF1B;&#x5982;&#x679C;&#x76F8;&#x4EA4;&#x90E8;&#x5206;&#x662F;&#x4E00;&#x6761;&#x7EBF;&#xFF0C;&#x5219;&#x4E3A;&#x4E00;&#x7EF4;&#xFF0C;dim()=1&#xFF1B;&#x5982;&#x679C;&#x76F8;&#x4EA4;&#x90E8;&#x5206;&#x662F;&#x4E00;&#x4E9B;&#x70B9;&#xFF0C;&#x5219;&#x4E3A;0&#x7EF4;&#xFF0C;dim()=0&#xFF1B;&#x5982;&#x679C;&#x4E0D;&#x76F8;&#x4EA4;&#xFF0C;&#x5219;dim()=-1;&#x4ECE;&#x4E0A;&#x5F80;&#x4E0B;&#xFF0C;&#x4ECE;&#x5DE6;&#x5F80;&#x53F3;&#x8BFB;&#x53D6;&#x8FD9;&#x4E2A;&#x77E9;&#x9635;&#xFF0C;&#x5C31;&#x4F1A;&#x6709;&#x4E00;&#x4E2A;&#x5B57;&#x7B26;&#x4E32;&#xFF0C;&#x5982;&quot;212101212&quot;&#xFF0C;&#x5373;&#x5C06;&#x76F8;&#x4E92;&#x5173;&#x7CFB;&#x8F6C;&#x6362;&#x6210;&#x4E86;&#x4E00;&#x4E2A;&#x5B57;&#x7B26;&#x4E32;&#xFF0C;&#x6700;&#x7EC8;&#x5BF9;&#x5B57;&#x7B26;&#x4E32;&#x8FDB;&#x884C;&#x5224;&#x65AD;&#x5C31;&#x53EF;&#x4EE5;&#x4E86;&#x3002;&#x4E0A;&#x9762;&#x7684;&#x56FE;&#x53EA;&#x662F;&#x8BB8;&#x591A;&#x5173;&#x7CFB;&#x4E2D;&#x7684;&#x4E00;&#x79CD;&#xFF0C;&#x753B;&#x7684;&#x662F;&#x76F8;&#x4EA4;&#x7684;&#x60C5;&#x5F62;&#xFF0C;&#x6240;&#x4EE5;&#x5E76;&#x6CA1;&#x6709;&#x51FA;&#x73B0;-1&#x7684;&#x60C5;&#x51B5;&#x3002;</p>
<p>&#x5982;&#x679C;&#x6362;&#x4E00;&#x79CD;&#x5199;&#x6CD5;&#xFF0C;&#x6211;&#x4EEC;&#x5C06;&#xFF08;0&#xFF0C;1&#xFF0C;2&#xFF09;&#x8BA4;&#x4E3A;&#x662F;&#x76F8;&#x4EA4;&#xFF0C;&#x5199;&#x4E3A;T&#xFF0C;-1&#x8BA4;&#x4E3A;&#x4E0D;&#x76F8;&#x4EA4;&#xFF0C;&#x5199;&#x4E3A;F&#x3002;&#x5219;&quot;212101212&quot;&#x53D8;&#x4E3A;&quot;TTTTTTTTT&quot;&#x3002; &#x5B9E;&#x9645;&#x4E0A;&#x8FD9;9&#x4E2A;&#x503C;&#xFF0C;&#x6211;&#x4EEC;&#x53EA;&#x9700;&#x8981;&#x77E5;&#x9053;&#x5176;&#x4E2D;&#x51E0;&#x4E2A;&#x503C;&#x5C31;&#x80FD;&#x4F5C;&#x51FA;&#x5224;&#x65AD;&#x4E86;&#xFF0C;&#x4E0D;&#x9700;&#x8981;&#x5168;&#x90E8;&#x77E5;&#x9053;&#x3002;&#x6BD4;&#x5982;&#x6211;&#x4EEC;&#x53EA;&#x8981;&#x77E5;&#x9053;&#x7B2C;&#x4E00;&#x4F4D;&#x662F;T&#xFF0C;&#x5C31;&#x80FD;&#x5224;&#x65AD;&#x4E24;&#x8005;&#x76F8;&#x4EA4;&#xFF0C;&#x800C;&#x540E;&#x9762;8&#x4F4D;&#x662F;&#x4EC0;&#x4E48;&#x5E76;&#x4E0D;&#x5173;&#x5FC3;&#x3002;&#x4E0D;&#x5173;&#x5FC3;&#x662F;&#x4EC0;&#x4E48;&#x503C;&#xFF0C;&#x6211;&#x4EEC;&#x5C31;&#x7528;<em>&#x6765;&#x4EE3;&#x66FF;&#xFF0C;&#x56E0;&#x6B64;&#xFF0C;&#x6211;&#x4EEC;&#x53EA;&#x8981;&#x770B;&#x5230;&quot;T<strong><em>*</em></strong></em>&quot;&#xFF0C;&#x5C31;&#x77E5;&#x9053;&#x4E24;&#x4E2A;&#x56FE;&#x5F62;&#x76F8;&#x4EA4;&#x3002;</p>
<p>&#x5C06;&#x5173;&#x7CFB;&#x7528;&#x4E13;&#x4E1A;&#x672F;&#x8BED;&#x6765;&#x8868;&#x8FBE;&#xFF0C;&#x6211;&#x4EEC;&#x5C31;&#x53EB;&#x8C13;&#x8BCD;&#xFF0C;&#x6BD4;&#x5982;&#x76F8;&#x4EA4;&#x3001;&#x63A5;&#x89E6;&#x3001;&#x91CD;&#x53E0;&#x3001;&#x5305;&#x542B;&#x7B49;&#x3002;&#x5173;&#x7CFB;&#x6BD4;&#x8F83;&#x591A;&#xFF0C;&#x5B9A;&#x4E49;&#x4E5F;&#x662F;&#x975E;&#x5E38;&#x7CBE;&#x7EC6;&#x3002;&#x6211;&#x4EEC;&#x8FD9;&#x91CC;&#x53EA;&#x8003;&#x8651;&#x4E24;&#x4E2A;&#x9762;&#xFF08;&#x4E24;&#x4E2A;&#x591A;&#x8FB9;&#x5F62;&#xFF09;&#x7684;&#x5173;&#x7CFB;&#xFF0C;&#x56E0;&#x6B64;&#xFF0C;&#x53EA;&#x9700;&#x8981;&#x638C;&#x63E1;&#x51E0;&#x79CD;&#x5173;&#x7CFB;&#x5C31;&#x53EF;&#x4EE5;&#x4E86;&#x3002;&#x5982;&#x679C;&#x9700;&#x8981;&#x5224;&#x65AD;&#x70B9;&#x3001;&#x7EBF;&#x5173;&#x7CFB;&#x7684;&#xFF0C;&#x5EFA;&#x8BAE;&#x53BB;<a href="https://en.wikipedia.org/wiki/DE-9IM" target="_blank">https://en.wikipedia.org/wiki/DE-9IM</a> &#x4ED4;&#x7EC6;&#x770B;&#x770B;&#xFF0C;&#x4ECB;&#x7ECD;&#x5F97;&#x975E;&#x5E38;&#x8BE6;&#x7EC6;&#x3002;</p>
<p>&#x9762;&#x4E4B;&#x95F4;&#x7684;&#x5173;&#x7CFB;&#xFF0C;&#x4E3B;&#x8981;&#x4E24;&#x79CD;&#xFF1A;&#x76F8;&#x4EA4;&#x548C;&#x8131;&#x79BB;&#xFF08;&#x4E0D;&#x76F8;&#x4EA4;&#xFF09;&#xFF0C;&#x76F8;&#x4EA4;&#x53C8;&#x5206;&#x4E3A;&#x63A5;&#x89E6;&#x3001;&#x91CD;&#x53E0;&#x3001;&#x8986;&#x76D6;&#x548C;&#x76F8;&#x7B49;&#x3002;</p>
<table>
<thead>
<tr>
<th>&#x8C13;&#x8BCD;</th>
<th>&#x8FD4;&#x56DE;&#x503C;</th>
<th>&#x63CF;&#x8FF0;</th>
</tr>
</thead>
<tbody>
<tr>
<td>&#x76F8;&#x7B49;&#xFF08;Equals)</td>
<td><code>T*F**FFF*</code></td>
<td>&#x8FB9;&#x754C;&#x4E0A;&#x7684;&#x70B9;&#x548C;&#x5185;&#x90E8;&#x7684;&#x70B9;&#x5168;&#x90E8;&#x91CD;&#x5408;&#x3002;&#x5C5E;&#x4E8E;&#x76F8;&#x4EA4;&#x7684;&#x4E00;&#x79CD;</td>
</tr>
<tr>
<td>&#x8131;&#x79BB;&#xFF08;Disjoint)</td>
<td><code>FF*FF****</code></td>
<td>&#x4E0D;&#x76F8;&#x4EA4;&#xFF0C;&#x4E0E;&#x76F8;&#x4EA4;&#x76F8;&#x53CD;</td>
</tr>
<tr>
<td>&#x63A5;&#x89E6;&#xFF08;Touches)</td>
<td><code>FT*******\F**T*****\F***T****</code></td>
<td>&#x53EA;&#x6709;&#x8FB9;&#x754C;&#x4E0A;&#x6709;&#x5171;&#x540C;&#x70B9;&#xFF0C;&#x5185;&#x90E8;&#x6CA1;&#x6709;&#x3002;&#x5C5E;&#x4E8E;&#x76F8;&#x4EA4;&#x7684;&#x4E00;&#x79CD;</td>
</tr>
<tr>
<td>&#x8986;&#x76D6;&#xFF08;Covers)</td>
<td><code>T*****FF*\*T****FF*\***T**FF*\****T*FF*</code></td>
<td>b&#x4E0A;&#x7684;&#x6BCF;&#x4E2A;&#x70B9;&#x90FD;&#x5728;a&#x4E0A;&#xFF08;&#x8FB9;&#x754C;&#x548C;&#x5185;&#x90E8;&#xFF09;&#xFF0C;&#x4E14;&#x6240;&#x6709;&#x70B9;&#x90FD;&#x4E0D;&#x5728;a&#x5916;&#x90E8;&#x3002;&#x5C5E;&#x4E8E;&#x76F8;&#x4EA4;&#x7684;&#x4E00;&#x79CD;</td>
</tr>
<tr>
<td>&#x91CD;&#x53E0;&#xFF08;Overlaps)</td>
<td><code>T*T***T**\1*T***T**</code></td>
<td>a&#x548C;b&#x76F8;&#x4EA4;&#xFF0C;&#x4E14;&#x5177;&#x6709;&#x4E00;&#x90E8;&#x5206;&#x5171;&#x540C;&#x70B9;&#xFF0C;&#x4F46;&#x4E0D;&#x662F;&#x5168;&#x90E8;&#x5185;&#x90E8;&#x70B9;&#x3002;&#x5C5E;&#x4E8E;&#x76F8;&#x4EA4;&#x7684;&#x4E00;&#x79CD;</td>
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